4 Answers
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Human Computer Interaction (and UX) takes a lot of cues from more general Product Design (see The Design of Everyday Things) and psychology, and the physical part of the interface is extremely important and a great deal of research has gone into designing the most common computing physical interfaces; the keyboard and mouse.

One of the most important fields of Psychology for UX/HCI is Sensation and Perception research. By knowing how humans percieve things we gain a better understanding of how the person works; this is important for all interactions, not just analog or just digital. Linguistics and natural speech are also of increasing importance. Talking with computers or more generally artificial services has always been awkward; products like Siri hope to remove this trouble.

I think the most important parts of UX and HCI apply not specifically to the analog or digital worlds; they apply to the world, full stop. This is mostly psychological stuff, in addition to understanding how the human body works. Interfaces like keyboards and mice are highly successful because of how well humans interact with them and they have a large body of research to back them up.

Very rarely does any real, helpful knowledge about UX only apply to the digital or analog worlds; people are the same in both. The main difference is that our experience in the analog world is much greater and easier to abstract to the analog world than the digital, meaning digital interactions are defacto much less natural. This, however, does not mean analog interactions are easy!

I would add Instrumentation as an interesting field, which involves many different trades and professions such as instrumentation engineers, electricians, pipefitters, power engineers and mechanical engineers.

I think you summed things up in your question. Broadly speaking, I think the core disciplines could be grouped thusly:

Library Sciences

Visual Design

Human Factors

With specific job titles pulling from one or more of those broad categories.

Other than that, yes, most any job that is part of a process of delivering a goods or service has elements of UX, be it formally acknowledged or not. Regarding delivering services, service design may be of interest to you as it's an emergency field unto itself.